数学·结合·number·theory 模式

识别信号

• Look for the candidate’s understanding of prime number theory and palindrome detection.
• Pay attention to optimization strategies for both checking and searching for prime palindromes.
• The interviewer mentions factors are always between 1 and n, which points to a bounded divisor scan rather than anything probabilistic or recursive.

解题流程

1. 1. 明确窗口/状态定义
2. 2. 更新状态并维护约束
3. 3. 用边界样例验证

常见失分点

• Failing to optimize the prime checking process, leading to slow solutions.
• Double-counting sqrt(n) when n is a perfect square, which shifts the kth position and returns the wrong factor.
• Forgetting that even numbers return n itself, leading to unnecessary multiplication.